You will need to use a number of interesting tools from both packages working in the following order:
create a landscape in Bryce
Render as a 360deg panorama
In max- create a X-ref scene to use in your renders.
Apply the panoramic picture onto the environment in the Max scene
Set up the subject of your render- with the environment scene x-ref'd from an external scene.

Part -1

Set up your landscape in Bryce in the usual way. the examples I will use are intended for aircraft in flight scenes. So my scene has the camera positioned high up to give a good perspective. More down to earth scenes work just as well for a suitable theme.

Select camera- under attributes- A, set the field of view (FOV) to 180.
Under render properties- set the render type to 360 panorama render. This feature is slyly hidden under a small triangle near the trackball.

If you should hear of criticism of Bryce's interface- this is where the problem lies - function hidden under almost invisible little trianges, unlabelled and they don't even show up unless you roll over them with the mouse pointer.

Under File>Document setup: you need to produce a bitmap that is twice as wide as it is high- for example: 600 x 1200 pixels. this is because the map for the sphere needs to wrap from north to south (180 deg) then all the way around the equator (360 deg).

Camera setup- select the camera- make sure you are in Director's view to do this. Or select camera from the selection sub-menu on the bottom right of the screen. Once the camera is selected- click the little letter "A" next to the selection box- this is "attributes" which gives you access to various options
click: FOV to 180 deg
set camera to "locked"- (there's no need to set the composition apart from the altitude of the camera- it all gets rendered in the end).
Make sure the camera is horizontal & level- that is X= 0 deg, Z=0 deg Y can be whatever.

If you get this bit wrong - the result is like this